Create a surrogate model for the objective function for the three survey line example

If you are running this notebook locally, make sure you’ve followed steps here to set up the environment. (This environment.yml file specifies a list of packages required to run the notebooks)

# -------------------------------------------------------- #
#                                                          #
#     Uncomment below to set up environment on "colab"     #
#                                                          #
# -------------------------------------------------------- #

# !pip install -U cofi
# !pip install git+https://github.com/JuergHauser/PyP223.git
# !pip install smt
# !git clone https://github.com/inlab-geo/cofi-examples.git
# %cd cofi-examples/examples/vtem_max

# If this notebook is run locally PyP223 and smt need to be installed separately by uncommenting the following lines,
# that is by removing the # and the white space between it and the exclamation mark.
# !pip install git+https://github.com/JuergHauser/PyP223.git
# !pip install smt

import pickle
import numpy
import matplotlib.pyplot as plt
import cofi
import smt
import smt.sampling_methods
import smt.surrogate_models
import smt.utils.misc
import tqdm
from vtem_max_forward_lib import (
    problem_setup,
    system_spec,
    survey_setup,
    ForwardWrapper
)

numpy.random.seed(42)
numpy.set_printoptions()

Background

This example use the surrogate modelling toolbox to create a surrogate model for the objective function used in the synthetic example where we invert the vertical component of three survey lines of a VTEM max survey. This notebook employs the Kriging approach using the training and test samples generated here to create a surrogate model.

with open('three_survey_lines_lhs.npy', 'rb') as f:
    ndim=int(numpy.load(f))
    xlimits=numpy.load(f)
    xtrain=numpy.load(f)
    ytrain=numpy.load(f)
    xtest=numpy.load(f)
    ytest=numpy.load(f)

xlimits=xlimits.astype('double')
xtrain=xtrain[0:150].astype('double')
ytrain=ytrain[0:150].astype('double')
xtest=xtest[0:25].astype('double')
ytest=ytest[0:25].astype('double')

Training

# The variable 'theta0' is a list of length ndim.
t = smt.surrogate_models.KRG(theta0=[1e-2]*ndim,print_prediction = False)
t.set_training_values(xtrain,ytrain)
t.train()

___________________________________________________________________________

                                  Kriging
___________________________________________________________________________

 Problem size

      # training points.        : 100

___________________________________________________________________________

 Training

   Training ...
   Training - done. Time (sec):  3.7126794

Validation

# Prediction of the validation points
y = t.predict_values(xtest)
# Estimated variance for the validation points
s2 = t.predict_variances(xtest)
#plot with the associated interval confidence
yerr= 2*3*numpy.sqrt(s2) #in order to use +/- 3 x standard deviation: 99% confidence interval estimation

# Plot the function, the prediction and the 99% confidence interval based on
# the MSE
fig = plt.figure()
plt.plot(ytest, ytest, '-', label='$y_{true}$')
plt.plot(ytest, y, 'r.', label='$\\hat{y}$')
plt.errorbar(numpy.squeeze(ytest), numpy.squeeze(y), yerr=numpy.squeeze(yerr), fmt = 'none', capsize = 5, ecolor = 'lightgray', elinewidth = 1, capthick = 0.5, label='confidence estimate 99%')
plt.xlabel('$y_{true}$')
plt.ylabel('$\\hat{y}$')

plt.legend(loc='upper left')
plt.title('Validation of the model prediction with confidence estimates')
plt.show()

Save the surrogate model for subsequent use

filename = "kriging_surrogate_model.pkl"
with open(filename, "wb") as f:
   pickle.dump(t, f)

---

Watermark

watermark_list = ["cofi", "numpy", "scipy", "matplotlib","smt"]
for pkg in watermark_list:
    pkg_var = __import__(pkg)
    print(pkg, getattr(pkg_var, "__version__"))

cofi 0.2.11
numpy 2.3.5
scipy 1.17.0
matplotlib 3.10.8
smt 2.10.1

sphinx_gallery_thumbnail_number = -1